Noise for Discrete Synthesis. The segmentations we train the planning stage over are inherently discrete, while the generated layouts are soft and continuous. To maintain stable GAN training under these conditions, and inspired by the instance noise technique [1]}, we add a simple hierarchical noise map to the layouts fed into the discriminator, which helps ensuring its task remains challenging. We define the noise as \(\sum _{r=6}^{8} {\text{Upsample}({n}_{r}^{2^{r} \times 2^{r}}})\) , summing up noise grids \({n}_{r}\sim \mathcal {N}(0,\,\sigma ^{2})\)  across multiple resolutions, making it partly correlated between adjacent positions and more structured overall. This empirically enhances the effectiveness and substantially improves the generated layouts's quality.
